## unique numberThe constant U that results if a number _{n}A
consisting of _{n}n consecutive digits, in ascending order, is subtracted
from the number A' obtained by reversing the
digits of _{n}A. For example, a three-digit number
345, if subtracted from its reverse 543, yields a difference of 198. Any
other three-digit number subtracted from its reverse gives the same difference.
Thus _{n}U = 198. Similarly for a number with
four consecutive digits, the unique number _{3}U
= 3087. The first ten unique numbers are: _{4}U
= 0, _{1}U = 9, _{2}U
= 198, _{3}U = 3087, _{4}U
= 41976, _{5}U = 530865, _{6}U
= 6419754, _{7}U = 75308643, _{8}U
= 864197532, and _{9}U = 9753086421. Unique numbers
are related to Kaprekar numbers,
_{10}K, by the formula
_{n}For example, when n = 4, K = 6174,
_{4}K' = 4716, _{4}U
= 3087, _{4}U' = 7803, and
_{4}3087 + 7803 = 10890 = 6174 + 4716. ## Reference- Gupta, S. S. "Unique Numbers",
*Science Today*, January 1988, India.
## External siteShyam Sunder Gupta (unique numbers)## Related category• TYPES OF NUMBERS | |||||

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